{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from IPython import display\n",
    "from matplotlib import pyplot as plt \n",
    "import numpy as np\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 生成数据集\n",
    "\n",
    "构造一个简单的训练集，样本数为1000，特征个数为2。 线性回归的真实权重为$w = [2,-3.4]^T$ 偏差$b = 4.2$。随机生成的样本符合均值为0，标准差为1的正态分布，并且为其添加噪声，噪声服从均值为0，标准差为0.01的正态分布。\n",
    "然后生成第二个特征和标签的散点图，可以更直观的观测两者的线性关系。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([-0.6916,  1.0949]) tensor(-0.9040)\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.collections.PathCollection at 0x7ff11fd6ba90>"
     },
     "metadata": {},
     "execution_count": 20
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "num_inputs = 2\n",
    "num_examples = 1000\n",
    "true_w = [2,-3.4]\n",
    "true_b = 4.2\n",
    "\n",
    "features = torch.from_numpy(np.random.normal(0,1,(num_examples,num_inputs)))\n",
    "features = features.float()\n",
    "labels = true_w[0] * features[:,0] + true_w[1] * features[:,1] + true_b\n",
    "labels += torch.from_numpy(np.random.normal(0,0.01,size=labels.size()))\n",
    "\n",
    "print(features[0],labels[0])\n",
    "\n",
    "plt.scatter(features[:,1].numpy(),labels.numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 读取数据\n",
    "训练模型的时候，需要遍历数据集并不断的读取小批量样本数据。 这里定义一个函数，它每次返回`batch_size`（批量大小）个随机样本数据的特征和标签。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "tensor([[ 0.7581, -1.0815],\n        [-1.5533,  0.7440],\n        [-0.5597,  1.3104],\n        [-0.9394, -0.4327],\n        [ 0.4416, -0.6013],\n        [-0.9756,  0.8492],\n        [-0.7422,  0.7570],\n        [ 1.4515,  0.2212],\n        [ 1.0287, -0.2825],\n        [ 2.9517, -2.2948]], dtype=torch.float64) tensor([ 9.3859, -1.4323, -1.3622,  3.7979,  7.1306, -0.6544,  0.1663,  6.3339,\n         7.2233, 17.9116], dtype=torch.float64)\n"
    }
   ],
   "source": [
    "def data_iter(batch_size,features,labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples)) # 生成样本的index\n",
    "    random.shuffle(indices) # 洗牌，样本读取顺序是随机的\n",
    "    for i in range(0,num_examples,batch_size):\n",
    "        j = torch.LongTensor(indices[i:min(i + batch_size,num_examples)])\n",
    "        yield features.index_select(0,j),labels.index_select(0,j)\n",
    "\n",
    "batch_size = 10\n",
    "for X,y in data_iter(batch_size,features,labels):\n",
    "    print(X,y)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定义模型\n",
    "\n",
    "线性回归的模型的较为简单，就是一个矩阵的乘法。可以使用`torch.mm`做矩阵乘法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(X,w,b):\n",
    "    return torch.mm(X,w) + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定义损失函数\n",
    "使用平方损失来定义线性回归的损失函数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def squared_loss(y_hat,y):\n",
    "    return (y_hat - y.view(y_hat.size())) ** 2 / 2 # 这里返回的是向量"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定义优化算法\n",
    "使用小批量随机梯度下降算法，不断的迭代模型参数来优化损失函数。 这里自动求导模块计算得来的梯度是一个批量的梯度和，将它除以批量的大小来得到平均值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(params,lr,batch_size):\n",
    "    for param in params:\n",
    "        param.data -= lr * param.grad / batch_size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 初始化参数\n",
    "将权重参数初始化为均值为0，标准差为0.01的正态随机数，偏差初始化为0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([0.], requires_grad=True)"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "w = torch.tensor(np.random.normal(0,0.01,(num_inputs,1)),dtype=torch.float32)\n",
    "b = torch.zeros(1,dtype=torch.float32)\n",
    "\n",
    "w.requires_grad_(requires_grad=True)\n",
    "b.requires_grad_(requires_grad=True)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型训练\n",
    "在训练中，通过多次迭代优化模型的参数。在每次迭代中，根据当前读取的小批量数据样本，通过调用反向函数`backward`计算小批量的随机梯度，并调用优化算法`sgd`更新模型的参数。 **在每次更新完参数后，要将参数的梯度清零。**\n",
    "\n",
    "在一个迭代周期（epoch）中，会完整的遍历一次`data_iter`函数，将数据集中的样本都使用一次。 这里迭代的epoch次数以及学习速率`lr`都是超参数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch 1,loss 0.000046\nepoch 2,loss 0.000046\nepoch 3,loss 0.000046\n[2, -3.4] tensor([[ 1.9999],\n        [-3.4002]], requires_grad=True)\n4.2 tensor([4.1999], requires_grad=True)\n"
    }
   ],
   "source": [
    "lr = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg # 模型，也可以称为网络结构\n",
    "loss = squared_loss\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    for X,y in data_iter(batch_size,features,labels):\n",
    "        l = loss(net(X,w,b),y).sum()\n",
    "        l.backward()\n",
    "        sgd([w,b],lr,batch_size)\n",
    "\n",
    "        w.grad.data.zero_()\n",
    "        b.grad.data.zero_()\n",
    "    \n",
    "    train_l = loss(net(features,w,b),labels)\n",
    "    print('epoch %d,loss %f' % (epoch + 1,train_l.mean().item()))\n",
    "\n",
    "# 输出训练结果以及真实值\n",
    "print(true_w,w)\n",
    "print(true_b,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 总结\n",
    "\n",
    "线性回归的基本要素\n",
    "\n",
    "## 模型的定义\n",
    "定义一个（一组）函数来表示输入和输出的关系，这就是模型（model）。 在线性回归中，假设输入和输出之间的关系市线性的\n",
    "$$\n",
    "\\hat{y} = x_1\\cdot w_1 + x_2 \\cdot w_2 + b\n",
    "$$\n",
    "上面公式中，$w_1,w_2$是权重参数，$b$是偏差（bias），这就是线性回归模型中的参数。\n",
    "\n",
    "> 在深度学习中，网络的结构就相当于模型，每一个层相当于一个函数。\n",
    "\n",
    "## 模型的训练\n",
    "\n",
    "- 训练数据\n",
    "- 损失函数\n",
    "- 优化算法 在深度学习中，最常用的优化算法为小批量梯度下降算法（SGD，mini-batch stochastic gradient descent）。"
   ]
  }
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